We know that a very ample divisor gives us an embedding into projective space and that very ample divisors are exactly the hyperplane sections.
Is there a similar geometric intuition for ample divisors? I know that a line bundle is ample if and only if some tensored power of it is very ample, so a divisor is ample if $\exists n$ such that $nD \sim H$ for $H$ a hyperplane. But can I already get a map into projective space from an ample divisor that is, let's say injective, or an immersion?